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# Probabilistic quantification of tsunami current hazard using statistical emulation

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## Abstract

In this paper, statistical emulation is shown to be an essential tool for the end-to-end physical and numerical modelling of local tsunami impact, i.e. from the earthquake source to tsunami velocities and heights. In order to surmount the prohibitive computational cost of running a large number of simulations, the emulator, constructed using 300 training simulations from a validated tsunami code, yields 1 million predictions. This constitutes a record for any realistic tsunami code to date, and is a leap in tsunami science since high risk but low probability hazard thresholds can be quantified. For illustrating the efficacy of emulation, we map probabilistic representations of maximum tsunami velocities and heights at around 200 locations about Karachi port. The 1 million predictions comprehensively sweep through a range of possible future tsunamis originating from the Makran Subduction Zone (MSZ). We rigorously model each step in the tsunami life cycle: first use of the three-dimensional subduction geometry Slab2 in MSZ, most refined fault segmentation in MSZ, first sediment enhancements of seabed deformation (up to 60% locally) and bespoke unstructured meshing algorithm. Owing to the synthesis of emulation and meticulous numerical modelling, we also discover substantial local variations of currents and heights.
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... High-accuracy, highresolution computations are especially useful in tsunami modelling studies to assess inundation, damage to infrastructure and asset losses but also for evacuation modelling. The parameter space dimension is also typically high, and the number of expensive numerical simulations needed to resolve the statistics about the output tends to be large (on the order of thousands for a well-approximated distribution; Salmanidou et al., 2017;Gopinathan et al., 2021) and hard to materialize as it depends on the available resources, code architecture and other factors. ...
... We propose using a statistical surrogate approach, also called emulation, in which one approximates simulation outputs of interest as a function of the scenario parameter space. Such approaches have been implemented for uncertainty quantification of tsunami hazard at various settings (Sraj et al., 2014;Salmanidou et al., 2017Salmanidou et al., , 2019Guillas et al., 2018;Denamiel et al., 2019;Snelling et al., 2020;Gopinathan et al., 2021;Giles et al., 2021). ...
... This is done for the first time towards a realistic case using high-performance computing (HPC). A one-shot random sampling for the training (as for example in Salmanidou et al., 2017;Gopinathan et al., 2021;Giles et al., 2021) lacks the information gain achieved by sequential design. Concretely, sequential design can reduce by 50 % the computational cost, as demonstrated in Beck and Guillas (2016) for a set of toy problems, so applying this novel approach towards a realistic case is showcasing real benefits in the case of high resolution with a complex parametrization of the source. ...
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The potential of a full-margin rupture along the Cascadia subduction zone poses a significant threat over a populous region of North America. Previous probabilistic tsunami hazard assessment studies produced hazard curves based on simulated predictions of tsunami waves, either at low resolution or at high resolution for a local area or under limited ranges of scenarios or at a high computational cost to generate hundreds of scenarios at high resolution. We use the graphics processing unit (GPU)-accelerated tsunami simulator VOLNA-OP2 with a detailed representation of topographic and bathymetric features. We replace the simulator by a Gaussian process emulator at each output location to overcome the large computational burden. The emulators are statistical approximations of the simulator's behaviour. We train the emulators on a set of input–output pairs and use them to generate approximate output values over a six-dimensional scenario parameter space, e.g. uplift/subsidence ratio and maximum uplift, that represent the seabed deformation. We implement an advanced sequential design algorithm for the optimal selection of only 60 simulations. The low cost of emulation provides for additional flexibility in the shape of the deformation, which we illustrate here considering two families – buried rupture and splay-faulting – of 2000 potential scenarios. This approach allows for the first emulation-accelerated computation of probabilistic tsunami hazard in the region of the city of Victoria, British Columbia.
... Most of the novel techniques in the field of PTHA are based on the notion of reducing the number of required computational runs with the aid of Gaussian process emulators, which are capable of maintaining good output accuracy and uncertainty quantification. The investigations of Gopinathan et al. [20] and Salmanidou et al. [21] are good examples of this approach, where the former delivered millions of output predictions based on 300 numerically simulated earthquake-tsunami scenarios, and the latter produced 2000 output predictions at each prescribed location, examining 60 full-fledged simulations. ...
... Even so, it is common knowledge that expensive computational resources for an accurate PTHA study are the main downside. Recent work aimed at circumventing this problem makes use of stochastic approximations, called emulators, built upon a pre-computed training set [20,21,39]. An emulator can be seen as an interpolating operator of the map that assigns to each input parametric array its corresponding desired output through a fully fledged simulation. ...
... The effectiveness of an emulator approach is closely related to the construction of the training set, which is its core. In [20], the epicenter location and moment magnitude were sampled using the LHS method to simulate 300 scenarios and retrieve the maximum water height and maximum current velocity at several locations, which in turn constitute the basis for building the training set. In [21], the authors sampled a sevendimensional input space using a sequential design MICE algorithm to generate a training set of 60 simulated scenarios. ...
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The application of simulation software has proven to be a crucial tool for tsunami hazard assessment studies. Understanding the potentially devastating effects of tsunamis leads to the development of safety and resilience measures, such as the design of evacuation plans or the planning of the economic investment necessary to quickly mitigate their consequences. This article introduces a pseudo-probabilistic seismic-triggered tsunami simulation approach to investigate the potential impact of tsunamis in the southwestern coast of Spain, in the provinces of Huelva and Cádiz. Selected faults, probabilistic distributions and sampling methods are presented as well as some results for the nearly 900 Atlantic-origin tsunamis computed along the 250 km-long coast.
... Statistical emulation, let alone multi-fidelity emulation, in tsunami risk assessment is a relatively unexplored field although Giles et al. [2021] andGopinathan et al. [2021] have established an insightful framework in GP tsunami emulation and alternative approaches, e.g., polynomial chaos, can be found such as in [Giraldi et al., 2017]. More examples of GP emulation in tsunami simulation can be found in [Guillas et al., 2018, Gopinathan et al., 2020a, Salmanidou et al., 2019a, 2021a, Snelling et al., 2020. The drawbacks of these prior research is that (i) computational cost for generating training data can still be too expensive and (ii) most of their approaches lack flexible experimental design although Salmanidou et al. ...
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